# Flood inundation simulation in river basin using a shallow water model: application to river Yamuna, Delhi region

Article

DOI: 10.1007/s12572-012-0053-3

Gurusamy, S. & Jayaraman, G. Int J Adv Eng Sci Appl Math (2012) 4: 250. doi:10.1007/s12572-012-0053-3

## Abstract

River Yamuna is one of the major rivers of India and the largest tributary of the Ganga. The river faces the hazards of annual floods, susceptibility to erosion and adverse impact of anthropogenic factors. The Delhi stretch of the river Yamuna is located between 28°24′17″ and 28°53′00″N and between 76°50′24″ and 77°20′37″E. The area is more vulnerable to annual floods and apart from this the stretch has wide sandy beds bordered by high banks which are subjected to annual inundation. To estimate the inundation in the river banks, our previously developed mathematical model (Senthil et al., Appl Math Comput 216:2544–2558, 2010), based on unsteady, depth averaged shallow water equations is applied to this particular case study of Yamuna river. The model uses a coordinate transformation which enables the deforming boundaries to be transformed to fixed boundaries in the computational plane. The model is based on the finite difference scheme which is conditionally stable. The 2001 bank lines data of the river is taken as the input along with the actual discharge data of 2001 to predict the change in the width of the river. The average increase of 3.19 % (simulated) of the entire stretch compares well with the observed result of 3.87 %. The simulated results are in conformity with the observed data, the maximum increase in the width being found between the Nizamuddin–Noida toll bridge regions. The characteristics such as (i) spatial extent of the flood on the floodplain, (ii) depth of the flood water, (iii) velocity of the flood water and (iv) the time it takes for the flood water to spread, can be produced with the help of the simulated results such as flooded area, inundation-depth, inundation-time and flow-field. In other words these results can be used as a tool to produce hydrologic data of the river banks as well as to evaluate the effects on the river banks due to flooding.

### Keywords

Shallow water equations River flow inundation Coordinate transformation Yamuna river